Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+y &= -1 \\ -4x-8y &= 8\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-4x = 8y+8$ Divide both sides by $-4$ to isolate $x$ $x = {-2y - 2}$ Substitute this expression for $x$ in the first equation. $4({-2y - 2}) + y = -1$ $-8y - 8 + y = -1$ Simplify by combining terms, then solve for $y$ $-7y - 8 = -1$ $-7y = 7$ $y = -1$ Substitute $-1$ for $y$ in the top equation. $4x- 1 = -1$ $4x-1 = -1$ $4x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = -1$.